The smoothing functions of nonsmooth matrix valued functions play an important role in the smoothing Newton method. In this thesis, we introduce a generalized smoothing function of the nonsmooth matrix valued function on the base of the smoothing function of the scalar valued function. we first study the properties of the smoothing function of the vector valued function defined via convolution. We discuss the directional differentiability, semismoothness and strong semismoothness of the smoothing function of the vector valued function. The smoothing function of the matrix valued function inherits the properties of the corresponding smoothing function of the scalar valued function.